It comes as the European Broadcasting Union (EBU) and the BBC confirmed the annual competition would be hosted in the UK due to the ongoing conflict in Ukraine.
While Ukraine won the contest in May, the EBU said the event “regrettably” could not be held in the country, following the Russian invasion earlier this year.
Speaking on BBC Two's Newsnight, the singer, who performed Boom Bang-a-Bang at Eurovision in 1969, said the city was "music mad" and would make "the most fabulous hosts".
She said: “It has to be Glasgow because that's where I come from.
"They're so politically savvy, they're the most fabulous hosts, they absolutely are music mad.
"I think it would be just the most fabulous thing and I would be there. I just cannot wait."
A spokesperson for Glasgow City Council said the city was a “safe pair of hands” after hosting COP26 in November last year.
They said: “Since it became a possibility that the UK might host on behalf of Ukraine, we’ve been working hard on our bid.
“We know we meet all the technical requirements and we know Glaswegians are desperate to welcome the world with open arms.
“Time is now really short to organise the contest and, having recently hosted COP, we know Glasgow is the safest of safe pairs of hands.”
Aberdeen is the only other Scottish city to have confirmed a bid for the event.
A spokesperson for the council said: “We were disappointed to learn that Eurovision 2023 cannot take place in Ukraine.
“Aberdeen has a track record of delivering major international events and now that the EBU has confirmed that the BBC will host the 2023 Eurovision song contest, we will look at the next steps in terms of the shortlisting process.
“The council has already instructed officers to continue the dialogue with relevant stakeholders and to look at the implications for the council of hosting this international event and its huge fanbase.
“The Eurovision Song Contest is a massive event with a worldwide audience.
“We have the city, the people and infrastructure to support international events such as this and it would provide a major boost to the Aberdeen and Scottish economies and raise the city’s profile with potential investors and visitors.”
Edinburgh hosted the contest at the Usher Hall in 1972 and has been the only Scottish city to do so.
Martin Osterdahl, the Eurovision Song Contest’s executive supervisor, said he was “grateful” to the BBC for hosting the contest next year.
“The BBC has taken on hosting duties for other winning countries on four previous occasions,” he said.
“Continuing in this tradition of solidarity, we know that next year’s contest will showcase the creativity and skill of one of Europe’s most experienced public broadcasters whilst ensuring this year’s winners, Ukraine, are celebrated and represented throughout the event.”